A 2.5 kg block of ice at a temperature of 0C and an initial speed of 5.7 m/s slides across a level floor. If 3.3*10^5 J are required to melt 1.0 kg of ice, how much ice melts, assuming that the initial kinetic energy of the ice block id entirely converted to the ice's internal energy?
initial KE= heat released
1/2 2.5*5.7^2=heat released.
heat released=massicemelted*3.3E5J/kg
solve for massicemelted
To solve this problem, we need to find the amount of kinetic energy (KE) possessed by the ice block and then compare it to the amount of energy required to melt the ice.
Step 1: Calculate the initial kinetic energy of the ice block.
The formula for kinetic energy is KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
Given:
Mass of ice block (m) = 2.5 kg
Initial speed (v) = 5.7 m/s
Using the formula, we can calculate the initial kinetic energy (KE) of the ice block:
KE = (1/2)(2.5 kg)(5.7 m/s)^2
KE = 81.675 J
Step 2: Calculate the amount of ice that can be melted with the initial kinetic energy.
Given:
Energy required to melt 1.0 kg of ice = 3.3 × 10^5 J
We can use the ratio of energy to melt 1.0 kg of ice and the initial kinetic energy to calculate the amount of ice melted.
Amount of ice melted = (Initial kinetic energy of ice block) / (Energy required to melt 1.0 kg of ice)
Amount of ice melted = 81.675 J / 3.3 × 10^5 J/kg
Amount of ice melted ≈ 0.000247 kg
Therefore, approximately 0.000247 kg of ice will melt, assuming that the initial kinetic energy of the ice block is entirely converted to the ice's internal energy.
To find out how much ice melts, we need to determine the change in kinetic energy and convert it to the ice's internal energy, which can then be used to calculate the amount of ice melted.
1. Determine the initial kinetic energy (KE) of the ice block:
- Mass of the ice block = 2.5 kg
- Initial speed = 5.7 m/s
- KE = 0.5 * mass * velocity^2
Plugging in the values:
KE = 0.5 * 2.5 kg * (5.7 m/s)^2
2. Calculate the change in kinetic energy by subtracting the initial kinetic energy from the total energy required to melt the ice:
- Change in KE = 3.3 * 10^5 J (energy required to melt 1.0 kg of ice) - Initial KE
3. Convert the change in kinetic energy to the internal energy (U) of the ice:
- Energy required to melt 1 kg of ice = 3.3 * 10^5 J
- Internal energy change = Change in KE / (Energy required to melt 1 kg of ice)
Plugging in the values:
Internal energy change = Change in KE / (3.3 * 10^5 J/kg)
4. Calculate the mass of the ice melted using the equation:
- Mass of ice melted = Internal energy change / (Energy required to melt 1 kg of ice)
Plugging in the values:
Mass of ice melted = Internal energy change / (3.3 * 10^5 J/kg)
By following these steps, you'll be able to determine how much ice melts.